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<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E24">XXTh1</font></span>: <a NAME="T17"><span class="comment"><font color="firebrick">:: ZMODUL04:17</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">V</font> being   <a href="vectsp_7.html#V3" title="VECTSP_7:attr.3">free</a>  <a href="zmodul01.html#NM1" title="ZMODUL01:NM.1">Z_Module</a><br/>  for <font color="Olive" title="b2">I</font>, <font color="Olive" title="b3">A</font> being   <a href="finset_1.html#V1" title="FINSET_1:attr.1">finite</a>  <a href="struct_0.html#NM2" title="STRUCT_0:NM.2">Subset</a> of <font color="Olive" title="b1">V</font>  st <font color="Olive" title="b2">I</font> is   <a href="zmodul03.html#NM1" title="ZMODUL03:NM.1">Basis</a> of <font color="Olive" title="b1">V</font> &amp; <span class="p1">(<span class="default"><a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b2">I</font></span>)</span> <a href="nat_1.html#K1" title="NAT_1:func.1">+</a> 1 <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="card_1.html#K4" title="CARD_1:func.4">card</a> <font color="Olive" title="b3">A</font> holds <br/><font color="Olive" title="b3">A</font> is  <a href="vectsp_7.html#NV2" title="VECTSP_7:NV.2">linearly-dependent</a> </div></div>
